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A garden hose can fill a swimming pool in 7 days, and a larger hose can fill the pool in 4 days. How long will it take to fill the pool if both hoses are used?

Respuesta :

ayalaanderson954

if the garden hose Takes 7 Days and the larger hose takes 4 days tan if You use voth of them it Will take 3 days

semsee45

Answer:

[tex]2 \frac{6}{11}\; \rm days\;[/tex]

2 days 13 hours 5 minutes 27 seconds

Step-by-step explanation:

First hose:

  • If the first hose can fill the pool in 7 days, then it can fill 1/7 of the pool in 1 day.

Second hose:

  • If the second hose can fill the pool in 4 days, then it can fill 1/4 of the pool in 1 day.

When both hoses are being used to fill the pool, their rates are additive:

[tex]\implies \dfrac{1}{7}+\dfrac{1}{4}=\dfrac{4}{28}+\dfrac{7}{28}=\dfrac{11}{28}[/tex]

Therefore, both hoses can fill 11/28 of the pool in 1 day.

To calculate how long it will take to fill the pool, divide 1 day by the combined rate:

[tex]\implies 1 \div \dfrac{11}{28}=1 \times \dfrac{28}{11}= \dfrac{28}{11}=2 \frac{6}{11}\; \rm days\;[/tex]

Therefore it takes 2 ⁶/₁₁ days to fill the pool if both hoses are used.

To find the time it takes in days, hours, minutes and seconds:

  • 6/11 days as hours is:
    [tex]\implies \dfrac{6}{11} \times 24=13\frac{1}{11}\; \rm hours[/tex]

  • 1/11 hours as minutes is:
    [tex]\implies \dfrac{1}{11} \times 60=5\frac{5}{11}\; \rm minutes[/tex]

  • 5/11 minutes as seconds is:
    [tex]\implies \dfrac{5}{11} \times 60=27.27\; \rm seconds[/tex]

Therefore, it takes:

  • 2 days 13 hours 5 minutes 27 seconds to fill the pool if both hoses are used (to the nearest second).

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